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Off-momentum DA of RCS 3D_BM & QFF & CC

AP meeting / December 8, 2004. Off-momentum DA of RCS 3D_BM & QFF & CC. Alexander Molodozhentsev Etienne Forest KEK. RCS_3DBM. Tune diagram. Structure resonances:. -Q X +2Q y =6 “Sextupole”. Chromatic tune_shift ~  0.08 (dp/p=  0.01). -Q x +3Q y =12 “Octupole”.

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Off-momentum DA of RCS 3D_BM & QFF & CC

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  1. AP meeting / December 8, 2004 Off-momentum DA of RCS3D_BM & QFF & CC Alexander Molodozhentsev Etienne Forest KEK

  2. RCS_3DBM Tune diagram Structure resonances: -QX+2Qy=6 “Sextupole” Chromatic tune_shift ~  0.08 (dp/p=  0.01) -Qx+3Qy=12 “Octupole” -Qx+4Qy=18 “Decapole” -Qx+5Qy=24 “Bare” tunes: Qx = 6.68 Qy = 6.27 --- scanning regions

  3. MADX:RCS Twiss parameters (dp=0.0) Wkin = 181 MeV …  = 0.54523 WHY? Because MADX uses ‘time” as the independent parameter instead of ‘path-length’… MAX_Dx ~ 10 m !!! MADX_Chromaticity: ~ -15 !!!

  4. RCS_3DBM Off-momentum particle motion(lattice#1) PTC tracking: Use “path” instead of “time”…SAD, MAD8 Observation point : SFX Dx ~ ??? p/p = 0.01 Dx (SFX) ~ 5.5 m PTC: Chromaticity (x/y) ~ -8 5.5 cm -15cm 15 cm

  5. Chromaticity definition Sextupole field component Path_length in ring If the code uses the time instead of the path, the chromaticity will be different in the case of the low kinetic energy: ds = (c) dt Wkin = 181 MeV …  = 0.54523 … then PATH ~ 0.545 TIME !!!

  6. Dispersion function definition Periodic dispersion function can be written as [Mario Conte, p.85] … also depends on choice “path” or “time” … MAD dispersion (“path”) is about two time bigger than SAD dispersion for Wkin=181 MeV …

  7. Off-momentum particle motion(lattice#1) PTC tracking: Use “time” instead of “path” …MADX Observation point : SFX Dx ~ 10 m p/p = 0.01 TDR: Bore radius of SFX is (330/2) mm=165 mm SFX: x ~ 13m, y ~ 6m xcenter->chamber ~ 16.5-10.0=6.5 cm x,MAX ~ (x)2 / x ~ (6.5e-2)2/13 ~ 325 .mm.mrad … Momentum Acceptance for p/p = 0.01 xp/p ~ 10 cm -15cm 15 cm

  8. RCS_3DBM Effects of the quadrupole fringe field ON-momentum particles… (1) ‘Octupole-like’ effect … … at the leading order – excitation of the normal octupole resonances OFF-momentum particles… (2) De-tuning effect for the off-momentum particles … … the end-field of the quadrupole magnet gives the beam two kicks in the opposite directions, which cancel for the paraxial trajectories, but which gives a net focusing to trajectories passing though at an angle. It means that the fringe field of the quadrupole magnets, which are located in the non- zero dispersion sections, will provide the de-tuning of the off-momentum particles. This effect depends on the particle momentum and the betatron amplitude, the dispersion and the slope of the dispersion at the location of the quadrupole magnet. (3) Sextupole feeding-down component … … for the off-momentum particles the pseudo-octupole nonlinearity of the quadrupole magnet will be “feeding-down” due to the closed orbit displacement in the quadrupole magnets in the non-zero dispersion regions (in the ARCs). In this case the quadrupole fringe field can contribute additional excitation to the normal sextupole resonances.

  9. RCS_3DBM Tune variation for off-momentum particles Linear chromaticity ~ (-8) Without sextupole magnets for the chromaticity correction…

  10. RCS_3DBM Off-momentum DA (3D_BM) 3D_BM Plus: QFFHE NO Sextupole CC Observation point: BM1 entrance (#47) dp/p=0

  11. RCS_3DBM Off-momentum DA (3D_BM) 3D_BM Plus: QFFHE Resonance [-1,2] driving terms NO Sextupole CC Observation point: BM1 entrance (#47) Resonance [-1,2] driving terms for this case is 3 times smaller than for the corresponding tunes of the on-momentum particles

  12. RCS_3DBM Off-momentum DA (3D_BM) 3D_BM Plus: QFFHE NO Sextupole CC Observation point: BM1 entrance (#47) Increasing the resonance 4Qx=27 for the off-momentum particles … by the feeding-down the high-order field components of the 3D_BM …

  13. RCS_3DBM Effect of the quadrupole fringe field for the off-momentum particles 3D_BM Plus: QFFHE NO Sextupole CC • Contribution to the normal • sextupole resonance by • the sextupole ‘feeding-down’ • of the QFF “pseudo-octupole”… • some compensation effect (1) (2) (2) Increasing of the normal octupole resonance…

  14. RCS_3DBM Off-momentum DA (3D_BM) 3D_BM Plus: QFFHE NO Sextupole CC Observation point: BM1 entrance (#47) Main limitation of the off-momentum DA is caused by the normal octupole resonance.

  15. Off-momentum DA (3D_BM):dp/p= 0.005

  16. Off-momentum DA (3D_BM):dp/p= 0.01

  17. … synchrotron oscillation … Some speculation … look at summary012-file …

  18. RCS_3DBM On-momentum particle motion NO CC Sextupoles Tune-scanning in the Qy direction QX – fix QY - vary Main limitation of the on-momentum DA is caused by the normal sextupole resonance

  19. RCS_3DBM Off-momentum (3D_BM) plus chromatic sextupole magnets Changing of the tune for different (dp/p) before (1) and after (2) the chromaticity correction

  20. RCS_3DBM Off-momentum DA after chromatic correction 3D_BM Plus: QFFHE Sextupole CC Observation point: BM1 entrance (#47) Twiss Parameters: (βx)1/2 = 2.7848 m1/2, x = 0.2517 (βy)1/2 = 3.9030 m1/2, y = 0.1990 (X=Y)MIN = 2.75 cm Ax = (Xmax)2x ~ 190  mm mrad Ay = (Ymax)2y ~ 150  mm mrad

  21. RCS_3DBM On-momentum DA after chromatic correction … result was presented October 27, 2004.

  22. RCS_3DBM To DO: • … correction of the normal sextupole resonance … • … off-momentum particle motion after the correction… Presented for the AP-group December 8, 2004

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